First measurements of the D+ parallel velocity, V∥D+, in L-mode discharges in the DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] tokamak boundary region at two poloidal locations, θ∼0° and θ∼255°, made using Mach probes, feature a peak with velocities of up to 80 km/s at the midplane last closed flux surface (LCFS), as high as ten times the charge exchange recombination C6+ toroidal velocity, VϕC6+, in the same location. The V∥D+ profiles are very asymmetric poloidally, by a factor of 8–10, and feature a local peak at the midplane. This peak, 1–2 cm wide, is located at or just inside the LCFS, and it suggests a large source of momentum in that location. This momentum source is quantified at ∼0.31 N m by using a simple momentum transport model. This is the most accurate measurement of the effects of so called “intrinsic” edge momentum source to date. The V∥D+ measurements are quantitatively consistent with a purely neoclassical computational modeling of V∥D+ by the code NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 50, 095010 (2008)], using VϕC6+ as input, for ρ∼0.7–0.95 at the two poloidal locations, where V∥D+ measurements exist. The midplane NEO-calculated V∥D+ grows larger than V∥C6+ in the steeper edge gradient region and trends to agreement with the probe-measured V∥D+ data near ρ∼1, where the local V∥D+ velocity peak exists. The measurements and computations were made in OH and L-mode discharges on an upper single null, with ion ∇BT drift away from the divertor. The rotating layer finding is similar in auxiliary heated discharges with and without external momentum input, except that at higher density the edge velocity weakens.